Proportional Editing mode in Object Mode?
What you describe is similar to Animation Nodes. 

This plugin allow to manipulate with objects based on algorithm, described by nodes.



Unfortunately, Animation Nodes is to difficult to explain in one post. But I give you a file, there you can start with.


(Note, you need to install Animation Nodes to view this file)

This is the nodes, that I used in the scene:



Here for every one object in my group (all cubes are in this group) it mix Initial transform and position of empty and set result to position of cubes.

Initial transform sets in T menu, here (select all objects and press From current transform):